6 research outputs found

    Symmetry structure in discrete models of biochemical systems : natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

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    © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.Interaction Computing (IC) is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are (1) to identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this, and (2) to use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in Systems Biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, Krebs cycle, and p53-mdm2 genetic regulation constructed from Systems Biology models have canonically associated algebraic structures { transformation semigroups. These contain permutation groups (local substructures exhibiting symmetry) that correspond to "pools of reversibility". These natural subsystems are related to one another in a hierarchical manner by the notion of "weak control ". We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-abelian groups (SNAGs) are found in biological examples and can be harnessed to realize nitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.Peer reviewe

    On straight words and minimal permutators in finite transformation semigroups.

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    “The original publication is available at www.springerlink.com”. Copyright SpringerMotivated by issues arising in computer science, we investigate the loop-free paths from the identity transformation and corresponding straight words in the Cayley graph of a finite transformation semigroup with a fixed generator set. Of special interest are words that permute a given subset of the state set. Certain such words, called minimal permutators, are shown to comprise a code, and the straight ones comprise a finite code. Thus, words that permute a given subset are uniquely factorizable as products of the subset's minimal permutators, and these can be further reduced to straight minimal permutators. This leads to insight into structure of local pools of reversibility in transformation semigroups in terms of the set of words permuting a given subset. These findings can be exploited in practical calculations for hierarchical decompositions of finite automata. As an example we consider groups arising in biological systems

    Annales Mathematicae et Informaticae 2010

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    Algebraic hierarchical decomposition of finite state automata : a computational approach

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    The theory of algebraic hierarchical decomposition of finite state automata is an important and well developed branch of theoretical computer science (Krohn-Rhodes Theory). Beyond this it gives a general model for some important aspects of our cognitive capabilities and also provides possible means for constructing artificial cognitive systems: a Krohn-Rhodes decomposition may serve as a formal model of understanding since we comprehend the world around us in terms of hierarchical representations. In order to investigate formal models of understanding using this approach, we need efficient tools but despite the significance of the theory there has been no computational implementation until this work. Here the main aim was to open up the vast space of these decompositions by developing a computational toolkit and to make the initial steps of the exploration. Two different decomposition methods were implemented: the VuT and the holonomy decomposition. Since the holonomy method, unlike the VUT method, gives decompositions of reasonable lengths, it was chosen for a more detailed study. In studying the holonomy decomposition our main focus is to develop techniques which enable us to calculate the decompositions efficiently, since eventually we would like to apply the decompositions for real-world problems. As the most crucial part is finding the the group components we present several different ways for solving this problem. Then we investigate actual decompositions generated by the holonomy method: automata with some spatial structure illustrating the core structure of the holonomy decomposition, cases for showing interesting properties of the decomposition (length of the decomposition, number of states of a component), and the decomposition of finite residue class rings of integers modulo n. Finally we analyse the applicability of the holonomy decompositions as formal theories of understanding, and delineate the directions for further research

    Annales Mathematicae et Informaticae (37.)

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    On the skeleton of a finite transformation semigroup

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    There are many ways to construct hierarchical decompositions of trans- formation semigroups. The holonomy algorithm is especially suitable for computational implementations and it is used in our software package. The structure of the holonomy decomposition is determined by the action of the semigroup on certain subsets of the state set. Here we focus on this structure, the skeleton, and investigate some of its properties that are crucial for understanding and for efficient calculations
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